However, they did not all come into being at once. The first one--a white E for gunnery--is the 1906 award. Others followed later.
Got the above from a pdf document. My phone automatically opens those with no way I have found to share a link on the internet. However, if you want me to email you the pdf file, leave a message here and I will happily send it to you.
What I can do is copy/paste the text part of the doc. (It is only a couple pages, and it does have images which won't paste here.)
Here is the first page. The second page deals with the uniform emblem, so I am not pasting it:
"History of the Navy “E”
In 1906 President Theodore Roosevelt ordered an "E" to be painted in white on
warship gun turrets for those crews that had performed well in the Spanish
American War thus establishing the Navy Excellence "E" for gunnery. The "E"
was also authorized for wear by the enlisted gun crews earning the award as a
round patch with a white “E” worn on the sleeve above the cuff. The placement was
moved to the upper right sleeve in the 1950s.
A red "E" for excellence in engineering and a green "E" for excellence in aviation
were similarly rewarded some years after the excellence in gunnery “E” was
Around 1938 a horizontal hash mark was added below the “E” for subsequent
awards. In 1957 the horizontal hash mark was changed to a diagonal hash mark.
In 1960, a gold “E” was authorized to represent the fifth award of the “E” and a
gold diagonal hash mark was authorized for each award after the fifth award.
At some point the “E” came to denote winning competition in readiness for battle
efficiency instead of the original “excellence” in Gunnery award and was referred to
as the Battle Efficiency “E” after that point. This occurred after 1947.
The Navy "E" Ribbon denotes permanent duty on ships or in squadrons that won
the battle efficiency competition after July 1, 1974. This ribbon replaces the "E"
patch previously sewn on the right sleeve of enlisted uniforms.
Daniel D. Smith, SCPO, USNR(ret)
: When did the USN start painting excellence
: awards on ships?